# PROBLEMS ON AVERAGE

Problems on Average :

In this section, you will learn how average problems can be solved easily.

The formula given below can be used to find average of the given values. ## Problems on Average - Examples

Example 1 :

Find the average of first 20 natural numbers which are divisible by 7.

Solution :

Step 1 :

The first natural number which is divisible by 7 is 7.

The next numbers which are divisible by 7 are 14, 21.....

Step 2 :

Write the first twenty natural numbers which are divisible by 7.

They are 7, 14, 21, 28........ up to 20 terms.

Step 3 :

Find the sum of all the above numbers.

=  7 + 14 + 21 + 28.........up to 20 term

Because all of the above numbers are divisible by 7, we can factor 7.

=  7(1 + 2 + 3 + 4 +.........+ 20)

=  7 ⋅ 210

=  1470

Step 4 :

Find the average.

Average  =  Sum of all 20 numbers / 20

Average  =  1470 / 20

Average  =  73.5

Hence average of first 20 natural numbers which are divisible by 7 is 73.5

Example 2 :

The average of four consecutive even numbers is 27. Find the largest of these numbers.

Solution :

Step 1 :

Let "x' be the first even number.

Then the four consecutive even numbers are

x, x + 2, x + 4, x + 6

Step 2 :

Average of the four consecutive even numbers is 27.

So, we have

(x + x + 2 + x + 4 + x + 6) / 4  =  27

(4x + 12)  =  108

4x  =  96

x  =  24

Then, the value of the largest number is

x + 6  =  24 + 6  =  30

Hence, the largest of the four consecutive even numbers is 30.

Example 3 :

There are two sections A and B of a class, consisting 36 and 44 students respectively. If the average weight of the section A is 40 kg and that of section B is 35 kg, find the average weight of the whole class.

Solution :

Step 1 :

For section A, average weight is 40 kg.

That is,

Sum of the weights of 36 students / 36  =  40

Multiply both sides by 36.

Sum of the weights of 36 students  =  40 ⋅ 36

Sum of the weights of 36 students  =  1440

Step 2 :

For section B, average weight is 35 kg.

That is,

Sum of the weights of 44 students / 44  =  35

Multiply both sides by 44.

Sum of the weights of 44 students  =  35 ⋅ 44

Sum of the weights of 44 students  =  1540

Step 3 :

Total weight of 80 students (whole class) is

=  1440 + 1540

=  2980

Step 4 :

Find the average weight of the whole class.

Average weight of the whole class is

=  Total weight / No. of students

=  2980 / 80

=  37.25 kg

Hence, the average weight of the whole class is 37.25 kg.

Example 4 :

In John's opinion, his weight is greater than 65 kg but less than 72 kg. His brother doesn't agree with John and he thinks that John's weight is greater than 60 kg but less than 70 kg. His mother's view is that his weight cannot be greater than 68 kg. If all are them are correct in their estimation, what is the average of different probable weights of John ?

Solution :

Let "x" be John's weight

Step 1 :

According to John, we have 65 < x < 72.

According to his brother, we have 60 < x < 70.

According to his mother, we have x ≤ 68.

Step 2 :

The values of "x" which satisfy all the above three  conditions are 66, 67 and 68.

Step 3 :

Average of the above three values is

=  Sum of the three values / 3

=  (66 + 67 + 68) / 3

=  201/3

=  67

Hence, the average of different probable weights of John is 67 kg.

Example 5 :

A batsman makes a score of 87 runs in the 17th match and thus increases his average by 3. Find the average score average after 16th match.

Solution :

Step 1 :

Let "x" be the average after 16th match.

Then, the average after 17th match is (x + 3).

Step 2 :

Average after 17 matches  =  x + 3

Total runs scored in 17 matches / 17  =  x + 3

Total runs scored in 17 matches  =  17(x + 3)

Total runs scored in 17 matches  =  17x + 51 ----- (1)

Step 3 :

Average after 16 matches  =  x

Total runs scored in 16 matches / 16  =  x

Total runs scored in 16 matches  =  16x

Given : Runs cored in 17th match  =  87

Then, total runs scored in 17 matches  =  16x + 87 -----(2)

Step 4 :

From (1) and (2),

17x + 51  =  16x + 87

x + 51  =  87

Subtract 51 from both sides.

x  =  36

Hence, the average score after 16th match is 36. After having gone through the stuff given above, we hope that the students would have understood how to solve problem on average.

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

You can also visit our following web pages on different stuff in math.

WORD PROBLEMS

Word problems on simple equations

Word problems on linear equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

Word problems on comparing rates

Converting customary units word problems

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6 